The 33-year-old midfielder's current deal expires at the end of the season.
If Taylor's terms are not renewed and West Brom are still keen, then it's hard to see him turning down a move to a side who are looking like they'll finish in the top eight of the Premier League come the end of the season.
The Scotland global has been ever-present for the Baggies since joining from Manchester United in 2015, featuring in all 83 Premier League matches.
West Brom boss Tony Pulis is confident Jake Livermore won't get carried away after his week away with England.
Manchester United will host West Bromwich Albion at Old Trafford in an important Premier League clash.
"I'm hoping I'll get more out of him". 'He's been fantastic after the condition he had and what he went through.
"Once he got himself to a level where he knew his fitness would come back it was always just a case of him getting a vehicle to drive", said Pulis.
'That has been us and we're delighted we've given him that opportunity because he has certainly repaid it hand over fist. He's been a great advert for the young players at this club'.
The veteran ever-present centre-back has scored six league goals so far in 2016/17, with West Brom well on course to equal their best ever Premier League finish of eighth.
"It's very pleasing. I'd like to thank the club, the gaffer and everyone here who helps me to stay fit to be able to play at this level", McAuley told WBA.co.uk.